Magic-wavelength Faraday probe measures spin continuously and without light shifts

摘要

We describe a dispersive Faraday optical probe of atomic spin which performsa weak measurement of spin projection of a quantum gas continuously for morethan one second. To date focusing bright far-off-resonance probes onto quantumgases has proved invasive, due to strong scalar and vector light shiftsexerting dipole and Stern-Gerlach forces. We show that tuning the probe nearthe magic-zero wavelength at 790 nm between the fine-structure doublet of$^{87}$Rb cancels the scalar light shift, and careful control of polarizationeliminates the vector light shift. Faraday rotations due to each fine-structureline reinforce at this wavelength, enhancing the signal-to-noise ratio for afixed rate of probe-induced decoherence. Using this minimally-invasive spinprobe we perform microscale atomic magnetometry at high temporal resolution.Spectrogram analysis of the Larmor precession signal of a single spinorBose-Einstein condensate measures a time-varying magnetic field strength with 1{\mu}G accuracy every 5 ms; or equivalently makes > 200 successive measurementseach at $10\,\mathrm{pT/\sqrt{Hz}}$ sensitivity.